My research focuses on computational methods for uncertainty quantification in highly complex simulations in science and engineering where the underlying model is described by partial differential equations (PDEs). The goal is the efficient discretisation and solution of PDEs with random coefficients.
Applications include, but are not limited to: groundwater flow simulations with random permeabilities, elasticity problems in structural mechanics etc.
- Stochastic Galerkin methods
- Multilevel Monte Carlo estimators
- Finite elements, in particular mixed elements
- Numerical Linear Algebra: iterative methods for linear systems, Krylov subspace methods
- Numerical methods for highdimensional problems